If E denotes expectation, the variance of a random variable X is given by
The following plot shows a function y which varies linearly with x. The value of the integral $I=\int\limits_1^2y\;dx$ is
For |x|<< 1, coth(x) can be approximated as
$\underset{\theta \to 0}{\mathrm{lim}}\frac{\mathrm{sin}\left(\theta /2\right)}{\theta}$ is
Which one of the following functions is strictly bounded?
For the function ${e}^{-x}$, the linear approximation around x = 2 is:
An independent voltage source in series with an impedance Z_{S} = R_{S} + jX_{S} delivers a maximum average power to a load impedance Z_{L} when
The RC circuit shown in the figure is
The electron and hole concentrations in an intrinsic semiconductor are n_{i} per cm^{3} at 300 K. Now, if acceptor impurities are introduced with a concentration of N_{A} per cm^{3} (where N_{A} >> n_{i}), the electron concentration per cm^{3} at 300 K will be
In a p^{+}n junction diode under reverse bias, the magnitude of electric field is maximum at
The correct full wave rectifier circuit is:
(A)
(B)
(C)
(D)
In a transconductance amplifier, it is desirable to have
X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two‘s complement format. The sum of X and Y represented in two‘s complement format using 6 bits is:
The Boolean function Y = AB + CD is to be realized using only 2-input NAND gates. The minimum number of gates required is:
If the closed-loop transfer function of a control system is given as $T\left(s\right)=\frac{s-5}{\left(s+2\right)\left(s+3\right)}$, then it is
If the Laplace transform of a signal y(t) is $Y\left(s\right)=\frac{1}{s\left(s-1\right)}$, then its final value is
If $R\left(\tau \right)$ is the autocorrelation function of a real, wide-sense stationary random process, then which of the following is NOT true?
If S(f) is the power spectral density of a real, wide-sense stationary random process, then which of the following is ALWAYS true?
A plane wave of wavelength $\lambda $ is traveling in a direction making an angle 30° with positive x-axis and 90° with positive y-axis. The $\overrightarrow{E}$ field of the plane wave can be represented as (E_{0} is constant)
If C is a closed curve enclosing a surface S, then the magnetic field intensity $\overrightarrow{H}$, the current density $\overrightarrow{J}$ and the electric flux density $\overrightarrow{D}$ are related by